Spectral Estimation Analysis with Different Segment Lengths

When considering three different values of L, we observe the following phenomena: with L=256 (3 data segments), L=128 (7 data segments), and L=64 (15 data segments). The spectral estimation plots for different L values, as shown in the figure above, demonstrate significant differences. Through windowing implementation (typically using functions like hamming() or hanning() in signal processing libraries), we effectively reduce false spectral peaks in the frequency spectrum, but simultaneously achieve additional smoothing of actual peaks. Therefore, for the L=64 case, the spectral line at ω=0.8π can be clearly identified, though the two adjacent spectral peaks remain difficult to distinguish. The L=128 case provides the best balance between separation capability and detection performance. As expected, the L=256 case yields superior results, where we can clearly distinguish the presence of three spectral lines and their relative amplitude relationships from the spectral estimation plot. Beyond Welch's method (which implements modified periodogram averaging with overlapping segments), alternative approaches such as Bartlett's method (using non-overlapping segment averaging) can be employed. These methods utilize periodogram averaging techniques for power spectrum estimation and can achieve satisfactory results in spectral analysis applications.